LCM is applied to two or more whole numbers and is used as an aid in adding or subtracting fractions.
For example, 2/3 + 3/8. In this case we take the denominators 3 and 8 and simply multiply them together to get 24. 24 is the LCM of the whole numbers 3 and 8.
But sometimes the numbers have a common factor: 2/3+3/8+5/6. We have three denominators and there are common factors. We have 3 which has no factors; then we have 8=2*2*2 and 6=2*3. The LCM is the smallest number that 3, 8 and 6 all divide into. How do we find it. We treat the factors as ingredients as in a cake and lay them out: 2, 2, 2, 3. By taking one or more of these we can make up 3, 8 and 6. The 3 is on its own; we take all of the twos to make 8=2*2*2 and we take a 2 and the 3 to make 6=2*3. So the ingredients are all we need to make the LCM=2*2*2*3=24. We solve the fraction by rewriting the original fractions in terms of the LCM: (2*8)/24+(3*3)/24+(5*4)/24=(16+9+20)/24=45/24=(3*15)/(3*8)=15/8.
Let's do another. 4/9+5/12. 9=3*3; 12=2*2*3 or 4*3. Ingredients: 2*2*3*3. From these ingredients we can make up 9=3*3 and 12=2*2*3, LCM=2*2*3*3=36. (4/9+5/12=(16+15)/36=31/36.)